# Profit Maximization Under Price Discrimination

The aim of the discriminating monopolist is to maximize profits. We can thus derive the condition of profit maximization under price-discrimination by extending the normal theory of the firm to a case where there are two or more markets instead of just one market. We can build up the theory of profit maximization on the basis of certain assumptions :

1. There are two markets A and B.
2. The aim of the monopolist is to maximize profits.
3. He enjoys monopoly position in both the markets.
4. The elasticity of demand for the product in the two markets is different (This is perhaps the most essential condition for price discrimination to be profitable). Price discrimination, according to Stonier and Hague “will be profitable only if elasticity of demand in one market is different from elasticity of demand in the other. In general, it will pay a monopolist to discriminate between two markets only if elasticity of demand in one market is different from elasticity of demand in the other.” Let us assume that the demand is relatively inelastic in market A and relatively elastic in market B.
5. We also assume that conditions do prevail for practicing price discrimination.
6. We also assume that the buyers in one market are not able to trade profitably by selling the good to the buyers in the other market.

Let us now analyse how the monopolist will determine the size of his total output and on what basis will he decide to distribute the output between the two markets A and B. What will be the price that he will charge in the two markets and how will he maximize his profits.

The condition for profit maximization is that the Marginal Revenue should equal Marginal Cost. However, the complication arises here because the producer is selling this product not in just one market but in two markets. Hence he is faced with the revenue structure in two markets. Given the marginal cost curve he aggregates the marginal revenue from market A and Market B and produces the output up-to the point where combined MR = MC. He then distributes his output between the two markets in such a way that marginal revenue from both the markets will be the same, for if the marginal revenue from one market is more than the marginal revenue from the other then he will sell more in the former market till the marginal revenue in that market equalizes the marginal revenue in the other. Once the output gets distributed in the two markets on the basis of equal marginal revenue from both the markets the price in each market is shown by the respective average revenue curves. Obviously the price in the market where demand is relatively inelastic will be higher than the price in the market where demand is relatively elastic. Hence price-discrimination will be profitable only when elasticities of demand are different in the two markets. There is no incentive for price-discrimination if the elasticity of demand is the same in both the markets.

Let us now assume that elasticity of demand is different in the two markets A and B. If the elasticity of demand is low in market A; i.e. demand is relatively inelastic, the price can be raised in market A. Since the demand is relatively inelastic it is insensitive to rise in price and hence if the price is raised it will not cause much fall in demand. If the demand is relatively elastic in market B it will pay the monopolist to lower the price in B and increase the sales substantially. Now as in Market A since elasticity of demand is low, a decrease in sales will reduce revenue insignificantly, whereas in market B a reduction in price will add significantly to the total revenue. It will be profitable for the monopolist to transfer goods from Market A to market B. He will continue to transfer units from market A to market B till that point where marginal revenues are equal in both the markets. “It is also essential that not only the MR should be the same in each market but that the MR should also be equal to MC of producing the whole output.” This then is the condition for equilibrium under discriminating monopoly.